That's a really nice pattern! So, if I understand it correctly, the sqrtgun dictates the timing of the rest of the pattern, causing each successive spaceship fired to be linearly longer than the previous, as the gap between successive outputs of the sqrtgun is linearly longer than the previous?

77topaz wrote:That's a really nice pattern! So, if I understand it correctly, the sqrtgun dictates the timing of the rest of the pattern, causing each successive spaceship fired to be linearly longer than the previous, as the gap between successive outputs of the sqrtgun is linearly longer than the previous?

Basically, yes.What confuses me is that the outputs are increasing but when I run the pattern the length sequence does not appear to be monotonous.Specifically, the 2nd one seemed shorter than the 1st, the 5th seemed shorter than the 4th, the 8th seemed shorter than the 7th, etc. in my test.

77topaz wrote:That's a really nice pattern! So, if I understand it correctly, the sqrtgun dictates the timing of the rest of the pattern, causing each successive spaceship fired to be linearly longer than the previous, as the gap between successive outputs of the sqrtgun is linearly longer than the previous?

Indeed. If you attached (say) a caber-tosser to the input instead, you would get a geometric progression of Cordership lengths. And then Alexey Nigin has some super-sparse guns which produce arbitrary terms of finite index in the Grzegorczyk hierarchy.

Attaching a primer would be even more fun -- lots of conjectures about prime gaps could be re-written in terms of the output of the resulting Cordergun.

BlinkerSpawn wrote:What confuses me is that the outputs are increasing but when I run the pattern the length sequence does not appear to be monotonous.Specifically, the 2nd one seemed shorter than the 1st, the 5th seemed shorter than the 4th, the 8th seemed shorter than the 7th, etc. in my test.

Yes, the sequence of emission times of the sqrtgun is the sum of a quadratic polynomial and a period-3 oscillatory term:

It doesn't really matter much in this case, but I'm trying to encourage people to link to the conwaylife.com reference copy of Dean Hickerson's and Paul Callahan's and Mark Niemiec's pages, where maintenance is most likely to be done going forward -- in this case,

The sequence of lengths is even harder to understand because of the semi-Snarks -- alternate outputs of the sqrtgun control the timing of the head and tail of the Cordership.

We could put an inline tremi-Snark in the sqrtgun output to fix the "problem" of occasionally decreasing lengths, I suppose. Or run the output through a universal regulator instead, to make the problem even more mysterious:

Perhaps a more elegant solution to adjusting the timing would be a block-pushing mechanism that kicks back a glider into a syringe--in other words, a timing-dependent 3G-to-G that gets pushed further away whenever the input signal enters, as a "conduit" that happens to be a single block.

Kazyan wrote:Perhaps a more elegant solution to adjusting the timing would be a block-pushing mechanism that kicks back a glider into a syringe--in other words, a timing-dependent 3G-to-G that gets pushed further away whenever the input signal enters, as a "conduit" that happens to be a single block.

Kazyan wrote:Perhaps a more elegant solution to adjusting the timing would be a block-pushing mechanism that kicks back a glider into a syringe--in other words, a timing-dependent 3G-to-G that gets pushed further away whenever the input signal enters, as a "conduit" that happens to be a single block.

Dave Greene built such a contraption on 26th December 2002.

Here it is feeding the infinite spaceship gun:

Meanwhile, I built a p80 version of the sqrtgun that doesn't have any of the mod 3 issues of the original. It could do with quite a bit of optimisation:

Because the pair of gliders that return from the block happen to be close to 80 ticks apart I found it very awkward to use them to delete a single glider from a NE p80 stream. Another annoying thing is that p80 streams heading SW cannot cross the 3 glider salvo without destroying it. If anyone can find any improvements to the mechanism it might be worth packing down to its minimal size.

calcyman wrote:Dave Greene built such a contraption on 26th December 2002.

Huh, thanks. If I'd wanted a device like that, I'm not sure I would have remembered where to look for it. That was one of the few medium-sized experiments with p8 reflector circuitry.

Obviously it doesn't really belong in a thread called "Stable signal converters" -- though one slightly strange thing about that kind of construction is that it's really just about as Hashlife-friendly as stable conduits are. It might not even be that much more difficult to construct with a slow salvo, if we ever wanted to deal with the headache of making sure the figure eights were all in the right phase. At one point around that time I was thinking that a p8-based metacell was a pretty good idea.

Here's a trivial patch to begin construction with the smallest possible Cordership in the series. It will only build one out of sixteen members in the infinite family, though. It would take a good bit more custom construction to build every member of the family, probably by splitting the drive gun's output into sixteen signals and delaying fifteen of them by various amounts... maybe using the doubler toolkit.

chris_c wrote:Meanwhile, I built a p80 version of the sqrtgun that doesn't have any of the mod 3 issues of the original... If anyone can find any improvements to the mechanism it might be worth packing down to its minimal size.

This kind of thing makes me want to connect all the streams back to one gun. I think I'll just stay away for the time being.

#C pure stable block pusher Dave Greene 7 September 2003#C pattern will increase its height by 1 and return the Herschel#C to its starting point every 4N^2 + 6845N generations (N=1, 2, 3...)#C Beehive-eating glider-to-Herschel converter at top left posted by#C Paul Callahan on 30 Apr 1997 [irrelevant note: a glider following#C closely 64+ steps after the first glider passes through unharmed.]#C The Herschel duplicator I think is new. Thanks are due to Hersrch#C for the nice connection from there back to the main diagonal.x = 623, y = 639, rule = 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What do you do with ill crystallographers? Take them to the mono-clinic!

calcyman wrote:Hakuna matata -- within the following year, you built a p1 counterpart (which is what I was originally searching for when I found the p8 sqrtgun by mistake)...

Yikes, that awful old thing. It used to be horribly painful to get gliders synchronized with stable circuitry.

I think that that stable pattern pattern used my very first-ever complete "hot-swappable" +/-8N adjustment toolkit. But that toolkit tended to produce such huge slow patterns (at least by 2003 standards) that it was seldom if ever used again.

I finally started doing some work on another stable signal converter. It's a glider-to-spacerake converter (which is a pretty weird signal. However, there is a problematic part that I'm currently stuck on. In the pattern below, I've replaced the problematic signals with guns. The pattern is quite a bit larger than what it needs to be, mostly because I've been trying to have a repeat time of 78:

The classifier script says those gliders' rating is Eo3/Ee1, which means they're in the Horrible Group of Four and you can't turn the splitter ninety degrees without switching to an Oe3 or Oo1 splitter.

As long as I pick an Eo3 splitter, carefully keep the same orientation, and use the splitter's NW-traveling glider for the NW-most glider in the above reference pattern, the connection works reasonably well on the first try:

That doesn't seem to string the converter out too much more. There might be a way to rework the splitter on the right, to use a different splitter type and cross the streams, so that the naturally slow SE output signal is the one that you want to be slow anyway. It might make sense to allow crossing signals of this type sometimes -- in cases where there's only a conflict if you have an impossibly close following signal, like below 78 ticks.

But really this design will be just fine the way it is!

Goldtiger997 wrote:On a different note, there are a lot of different spaceships with newly cheap syntheses that are looking good for making glider-to-spaceship converters out of.

After April it might be time to experiment with the new semi-cenark toolkit some more, for a few of the more expensive constructions that have really high repeat times anyway -- see if it's possible to really save significant space by having just one mega-splitter hooked up to a G0 signal duplicator.

Until mid-April I'll be spending a lot of my Life hours working on a six-minute presentation for this year's Gathering for Gardner (13) in Atlanta. Am trying not to get distracted by anything else until after that... though with the appearance of things like Sir Robin and the 2-engine Cordership this has been terribly difficult.

Not quite yet, according to the arbitrary definition for this thread -- but it's close.

The fourdifferentstableglider-to-5c/9 converters are enough to prove that the converter is a viable one. It will be nice when someone digs up a direct H-to-LoM converter that can connect to it, but synchronizing gliders isn't too bad.

However, the whole exercise is currently useless, because there's no known way to get a signal back out of the 5c/9 wire. I'm currently limiting this thread to signals that are in some way interchangeable with each other. That is to say, for any two signal types X and Y, there have to be known ways to get from X to Y and also from Y back to X.

It's an annoying limitation, but without it it would be hard to know what goes on the list and what doesn't -- could end up with thousands of dead-end "signals".

The LoM-to-5c/9 seems unusually promising, though, so I've put it in a new "Hopeful candidates" section at the top of this thread.

Oddly enough, a design that catalyzed the entire half-X66-with-HWSS to produce a single output glider, then routes the glider through a G-to-HWSS, will have a much better repeat time -- though that would slow down the HWSS, of course, unless we add a lightspeed telegraph which let's not.

In this case it was four ticks off, so I replaced the d0 adjustment circuit with one of the two d4s, moved the rectifier a little farther away, and it worked like a charm.

Looks like this is a fairly slow d4 -- no doubt we can do better. That timing-adjuster collection is over two years old, and there are definitely a *lot* of new fast G-to-G circuits that could be collected and categorized, if anyone wants an enormously fun and rewarding project.

On my way to make a glider-to-spacerake converter, I thought I'd do a single extra signal split to create a stable glider-to-ecologist. Sadly, although the repeat time of the circuitry is 78 ticks, the synthesis' repeat time is 87 ticks. I'd forgotten how sparky ecologists are. Here is the converter, with a p87 gun attached:

dvgrn wrote:After April it might be time to experiment with the new semi-cenark toolkit some more, for a few of the more expensive constructions that have really high repeat times anyway -- see if it's possible to really save significant space by having just one mega-splitter hooked up to a G0 signal duplicator.

Until mid-April I'll be spending a lot of my Life hours working on a six-minute presentation for this year's Gathering for Gardner (13) in Atlanta. Am trying not to get distracted by anything else until after that... though with the appearance of things like Sir Robin and the 2-engine Cordership this has been terribly difficult.

Okay, I've finished the gilder-to-spacerake converter now, which doesn't really count as relatively soon, but I was busy with other things.

But first, when I had one more connection left, I had the fairly obvious realization that flipping the glider-to-lwss-pair part would decrease the bounding boxSo I did that to both the glider-to-ecologist and the glider-to-spacerake converters.

Looks really good! In your constructions I used to be able to trace the lengths of glider paths in the LifeHistory version and sometimes find trivial reductions. But not so often recently -- and not in this case!

I can see places that I might want to target first if I wanted to try rebuilding a big part of the structure from scratch. But with no guarantees that the result will actually turn out to be smaller... I think I'll just say it's perfect as it is.

dvgrn wrote:ooks really good! In your constructions I used to be able to trace the lengths of glider paths in the LifeHistory version and sometimes find trivial reductions. But not so often recently -- and not in this case!

Thanks a lot! Yeah, I tried harder this time to make sure everything was optimized before continuing with the next thing, and it seems to have paid off.

I decided to experiment with the new still in development doubled-signal toolkit. It was quite interesting to use. After a bit of playing around and logical thinking, I sort of worked out a way of using it fairly fast. In fact, significantly faster than the other toolkit, so I may be using this one where applicable again .

I tried it on the larger salvo from dvgrn's half-finished loafer v-gun. Unfortunately, the very last signal for me was also the CP-4 case, so it's a bit bigger than it was looking like it was going to be. However, its still fairly small for a one sided synchronization of seven signals, and it uses its bounding box well.

Anyway, I shamelessly borrowed permanently dvgrn's converter for the other loafer v-gun salvo (In the above linked post) to combine with mine. (@dvgrn sorry if you already had plans for it.) After that, it did not take long to create a stable v-gun glider-to-loafer converter:

Goldtiger997 wrote:I decided to experiment with the new still in development doubled-signal toolkit. It was quite interesting to use. After a bit of playing around and logical thinking, I sort of worked out a way of using it fairly fast. In fact, significantly faster than the other toolkit, so I may be using this one where applicable again :) .

Oh, good. If just a few more pieces show up with a few more different timings, that CP-4 case should stop being a problem, and then we'll have a really nice toolkit.

Goldtiger997 wrote:...it did not take long to create a stable v-gun glider-to-loafer converter...

Wow, that's a really nice example of the double-signal toolkit -- great work! It still seems as if there should be some clever re-folding of the signal paths in some counterintuitive way to take up less space, but I guess we can leave that for the time being as a challenge for interested readers... I can see a few places where I'm pretty sure I can save columns or rows, but nothing particularly interesting really.

Goldtiger997 wrote:@dvgrn, Do you think we could have an update for the original post.

Done. At least, I've added links for the new loafer con-V-erter, and the G-to-ecologist and G-to-spacerake. I think that gets us back up to date again. If there are other known interchangeable signals that are missing from the list, just let me know --

Well enough, I think. Attendees included Richard Guy, Bill Gosper, Rich Schroeppel, and Tom Rokicki, and none of them seemed to have any complaints about what I said.

Not sure when the video will show up on YouTube, but it will probably be there in something less than two years. Not surprisingly, I was too busy improvising around early microphone issues and a surprise introduction by the moderator to have any clear memory of what I actually said. So it will be interesting to see if I made any big mistakes. I did run out of time at the end, but I got six out of seven LifeViewer animations played and (somewhat) explained, and that's pretty good considering.

I should probably put together the fifteen-minute video that the talk would have come out to if I hadn't been limited to six minutes -- but I think I'll wait and see how the current version comes out first.

EDIT: Here's a first attempt at a minor size reduction. No really big changes. Maybe it doesn't quite count as a V-gun any more, since it's not all edge-shooters. But really there's no reason the first glider added to each salvo should have to be run through an edge shooter, unless (possibly) the spaceship being constructed is a diagonal traveler and the V-gun itself is supposed to be able to edge-shoot its spaceships.

I kind of like the increased clearance in this model, so I left off the construction area at the top. If you include that, the bounding box is now 600x647:

dvgrn wrote:Here's a first attempt at a minor size reduction. No really big changes... the bounding box is now 600x647...

Now down to 545x541, if you don't include the construction area at the top. No doubt it can go quite a bit smaller -- there's just one main sticky spot on each side, and no doubt if enough creativity is applied those can be avoided somehow.